• Structural Engineering and Mechanics
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• v.61 no.4
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• pp.497-510
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• 2017

A framed structure may be composed of two sub-structures, which are linked by a hinged joint. One sub-structure is the primary system and the other is the secondary system. The primary system, which is subjected to the periodic external load, can give rise to an auto-parametric resonance of the second system. Considering the geometric-stiffness effect produced by the axially internal force, the element equation of motion is derived by the extended Hamilton's principle. The element equations are then assembled into the global non-homogeneous Mathieu-Hill equations. The Newmark's method is introduced to solve the time-history responses of the non-homogeneous Mathieu-Hill equations. The energy-growth exponent/coefficient (EGE/EGC) and a finite-time Lyapunov exponent (FLE) are proposed for determining the auto-parametric instability boundaries of the structural system. The auto-parametric instabilities are numerically analyzed for the two frames. The influence of relative stiffness between the primary and secondary systems on the auto-parametric instability boundaries is investigated. A phenomenon of the "auto-parametric internal resonance" (the auto-parametric resonance of the second system induced by a normal resonance of the primary system) is predicted through the two numerical examples. The risk of auto-parametric internal resonance is emphasized. An auto-parametric resonance experiment of a ${\Gamma}$-shaped frame is conducted for verifying the theoretical predictions and present calculation method.

• Investigative Magnetic Resonance Imaging
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• v.9 no.1
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• pp.30-35
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• 2005

Purpose : The purpose of this study is to observe the blood oxygen level dependent (BOLD) contrast changes due to the reaction of human brain at a gustatory sense in response to a salty-taste stimulation. Materials and Methods : Twelve healthy, non-smoking, right-handed male subjects (mean age: 25.6, range: 23-28 years) participated in this salty-taste stimulus functional magnetic resonance (fMRI) study. MRI scans were performed with 1.57 GE Signa, using a multi-slice GE-EPI sequence according to a blood-oxy-gen-level dependent (BOLD) experiment paradigm. Scan parameters included matrix size $128\times128$, FOV 250 mm, TR 5000 msec, TE 60 msec, TH/GAP 5/2 mm. Sequential data acquisitions were carried out for 42 measurements with a repetition time of 5 sec for each taste-stimulus experiments. Analysis of fMRI data was carried out using SPM99 implemented in Matlab. NaCl solution $(3\%)$ was used as a salty stimulus. The task paradigm consisted of alternating rest-stimulus cycles (30-second rest, 15-second stimulus) for 210 seconds. During the stimulus period, NaCl-solution was presented to the subject's mouth through plastic tubes as a bolus of delivered every 5 sec using -processor controlled auto-syringe pump. Results : Insula, frontal opercular taste cortex, amygdala and orbitofrontal cortex (OFC) were activated by a salty-taste stimulation $(NaCl,\;3\%)$ in the fMRI experiments. And dosolateral prefrontal cortex (DLPFC) was also significantly responded to salty-taste stimuli. Activation areas of the right side hemisphere were more superior to the left side hemisphere. Conclusion : The results of this study well correspond to the fact that both insula, amygdala, OFC, DLPFC areas are established as taste cortical areas by neuronal recordings in primates. Authors found that laboratory-developed auto-syringe pump is suitable for gustatory fMRI study. Further research in this field will accelerate to inquire into the mechanism of higher order gustatory process.